Final Project: Economic Freedom of the World
Group1
2/16/2020
install.packages("caret",repos = "http://cran.us.r-project.org")## package 'caret' successfully unpacked and MD5 sums checked
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## The downloaded binary packages are in
## C:\Users\mjone\AppData\Local\Temp\RtmpwD0YEm\downloaded_packagespacman::p_load(pacman,janitor,readr,gmodels,tidyr,dplyr,ggthemes,gapminder,plotly,cowplot,tmap,ggplot2,RColorBrewer,gganimate,gifski,sf,factoextra,e1071,cluster,kernlab,corrplot,corrgram,hrbrthemes,viridis,glmnet,rpart,rpart.plot,partykit,maps,tmap,ggmap,htmltools,animation) Introduction
For our final project we will be reviewing Economic Freedom across the worls. With data ranging from 1970-2016.
Topics Covered: * Exploratory Analysis (Summaries and Filtered Data Frames) * Exploratory Plots * Linear Regression * Variable Selection: Lasso Method * Clustering
Step 1: We start by reading in and cleaning the data. In total we have 3726 observations
freedom <- read_csv("C:\\Users\\mjone\\OneDrive\\Desktop\\MBA 8045\\Data\\efw_cc.csv") # Update to your file location
freedom <- freedom %>%
clean_names()Now that we have access to all of our data we will take a look at it to see which variables we have access to
str(freedom)#3726 Observations## Classes 'spec_tbl_df', 'tbl_df', 'tbl' and 'data.frame': 3726 obs. of 36 variables:
## $ year : num 2016 2016 2016 2016 2016 ...
## $ iso_code : chr "ALB" "DZA" "AGO" "ARG" ...
## $ countries : chr "Albania" "Algeria" "Angola" "Argentina" ...
## $ economic_freedom : num 7.54 4.99 5.17 4.84 7.57 7.98 7.58 6.49 7.34 7.56 ...
## $ rank : num 34 159 155 160 29 10 27 106 49 30 ...
## $ quartile : num 1 4 4 4 1 1 1 3 2 1 ...
## $ x1a_government_consumption : num 8.23 2.15 7.6 5.34 7.26 ...
## $ x1b_transfers : num 7.51 7.82 8.89 6.05 7.75 ...
## $ x1c_gov_enterprises : num 8 0 0 6 8 10 10 0 7 10 ...
## $ x1d_top_marg_tax_rate : num 8 4.5 9.5 4 5 5 3.5 6.5 10 10 ...
## $ x1_size_government : num 7.94 3.62 6.5 5.35 7 ...
## $ x2a_judicial_independence : num 2.67 4.19 1.84 3.69 3.87 ...
## $ x2b_impartial_courts : num 3.15 4.33 1.97 2.93 4.2 ...
## $ x2c_protection_property_rights : num 4.51 4.69 2.51 4.26 5.66 ...
## $ x2d_military_interference : num 8.33 4.17 3.33 7.5 5.83 ...
## $ x2e_integrity_legal_system : num 4.17 5 4.17 3.33 5 ...
## $ x2f_legal_enforcement_contracts : num 4.39 4.51 2.3 3.63 5.2 ...
## $ x2g_restrictions_sale_real_property: num 6.49 6.63 5.46 6.86 9.8 ...
## $ x2h_reliability_police : num 6.93 6.14 3.02 3.39 5.71 ...
## $ x2i_business_costs_crime : num 6.22 6.74 4.29 4.13 7.01 ...
## $ x2j_gender_adjustment : num 0.949 0.821 0.846 0.769 1 ...
## $ x2_property_rights : num 5.07 4.69 2.96 3.9 5.81 ...
## $ x3a_money_growth : num 8.99 6.96 9.39 5.23 9.08 ...
## $ x3b_std_inflation : num 9.48 8.34 4.99 5.22 9.26 ...
## $ x3c_inflation : num 9.74 8.72 3.05 2 9.75 ...
## $ x3d_freedom_own_foreign_currency : num 10 5 5 10 10 10 10 5 0 10 ...
## $ x3_sound_money : num 9.55 7.25 5.61 5.61 9.52 ...
## $ x4a_tariffs : num 8.96 6.87 6.99 6.42 8.55 ...
## $ x4b_regulatory_trade_barriers : num 7.49 2.48 2.02 4.81 7.19 ...
## $ x4c_black_market : num 10 5.56 10 0 10 ...
## $ x4d_control_movement_capital_ppl : num 6.41 1.59 2.04 4.7 6.83 ...
## $ x4_trade : num 8.21 4.13 5.26 3.98 8.14 ...
## $ x5a_credit_market_reg : num 7.1 5.1 7.06 5.42 9.1 ...
## $ x5b_labor_market_reg : num 6.92 5.03 4.56 5.15 6.23 ...
## $ x5c_business_reg : num 6.71 5.68 4.93 5.54 6.8 ...
## $ x5_regulation : num 6.91 5.27 5.52 5.37 7.38 ...
## - attr(*, "spec")=
## .. cols(
## .. year = col_double(),
## .. ISO_code = col_character(),
## .. countries = col_character(),
## .. `ECONOMIC FREEDOM` = col_double(),
## .. rank = col_double(),
## .. quartile = col_double(),
## .. `1a_government_consumption` = col_double(),
## .. `1b_transfers` = col_double(),
## .. `1c_gov_enterprises` = col_double(),
## .. `1d_top_marg_tax_rate` = col_double(),
## .. `1_size_government` = col_double(),
## .. `2a_judicial_independence` = col_double(),
## .. `2b_impartial_courts` = col_double(),
## .. `2c_protection_property_rights` = col_double(),
## .. `2d_military_interference` = col_double(),
## .. `2e_integrity_legal_system` = col_double(),
## .. `2f_legal_enforcement_contracts` = col_double(),
## .. `2g_restrictions_sale_real_property` = col_double(),
## .. `2h_reliability_police` = col_double(),
## .. `2i_business_costs_crime` = col_double(),
## .. `2j_gender_adjustment` = col_double(),
## .. `2_property_rights` = col_double(),
## .. `3a_money_growth` = col_double(),
## .. `3b_std_inflation` = col_double(),
## .. `3c_inflation` = col_double(),
## .. `3d_freedom_own_foreign_currency` = col_double(),
## .. `3_sound_money` = col_double(),
## .. `4a_tariffs` = col_double(),
## .. `4b_regulatory_trade_barriers` = col_double(),
## .. `4c_black_market` = col_double(),
## .. `4d_control_movement_capital_ppl` = col_double(),
## .. `4_trade` = col_double(),
## .. `5a_credit_market_reg` = col_double(),
## .. `5b_labor_market_reg` = col_double(),
## .. `5c_business_reg` = col_double(),
## .. `5_regulation` = col_double()
## .. )summary(freedom)## year iso_code countries economic_freedom
## Min. :1970 Length:3726 Length:3726 Min. :1.970
## 1st Qu.:1995 Class :character Class :character 1st Qu.:5.855
## Median :2005 Mode :character Mode :character Median :6.680
## Mean :2001 Mean :6.520
## 3rd Qu.:2011 3rd Qu.:7.350
## Max. :2016 Max. :9.190
## NA's :723
## rank quartile x1a_government_consumption x1b_transfers
## Min. : 1.00 Min. :1.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 33.00 1st Qu.:1.000 1st Qu.: 4.450 1st Qu.: 6.208
## Median : 66.00 Median :3.000 Median : 6.082 Median : 8.432
## Mean : 68.31 Mean :2.498 Mean : 5.862 Mean : 7.673
## 3rd Qu.:102.00 3rd Qu.:3.000 3rd Qu.: 7.571 3rd Qu.: 9.482
## Max. :162.00 Max. :4.000 Max. :10.000 Max. :10.000
## NA's :723 NA's :723 NA's :589 NA's :960
## x1c_gov_enterprises x1d_top_marg_tax_rate x1_size_government
## Min. : 0.000 Min. : 0.000 Min. :0.6538
## 1st Qu.: 4.000 1st Qu.: 4.000 1st Qu.:5.2294
## Median : 7.000 Median : 6.000 Median :6.3197
## Mean : 5.738 Mean : 5.813 Mean :6.2321
## 3rd Qu.: 8.000 3rd Qu.: 8.000 3rd Qu.:7.2677
## Max. :10.000 Max. :10.000 Max. :9.9047
## NA's :646 NA's :1047 NA's :647
## x2a_judicial_independence x2b_impartial_courts x2c_protection_property_rights
## Min. :0.000 Min. :0.000 Min. : 0.000
## 1st Qu.:3.259 1st Qu.:3.352 1st Qu.: 4.093
## Median :4.698 Median :4.333 Median : 5.299
## Mean :5.019 Mean :4.675 Mean : 5.487
## 3rd Qu.:6.823 3rd Qu.:5.857 3rd Qu.: 7.058
## Max. :9.817 Max. :9.686 Max. :10.000
## NA's :1553 NA's :1179 NA's :1129
## x2d_military_interference x2e_integrity_legal_system
## Min. : 0.000 Min. : 0.000
## 1st Qu.: 4.500 1st Qu.: 4.167
## Median : 6.667 Median : 6.667
## Mean : 6.510 Mean : 6.200
## 3rd Qu.: 8.333 3rd Qu.: 8.333
## Max. :10.000 Max. :10.000
## NA's :1186 NA's :1153
## x2f_legal_enforcement_contracts x2g_restrictions_sale_real_property
## Min. :0.000 Min. :0.000
## 1st Qu.:3.376 1st Qu.:6.001
## Median :4.492 Median :7.528
## Mean :4.449 Mean :7.045
## 3rd Qu.:5.583 3rd Qu.:8.523
## Max. :8.479 Max. :9.981
## NA's :1361 NA's :1384
## x2h_reliability_police x2i_business_costs_crime x2j_gender_adjustment
## Min. :0.000 Min. :0.000 Min. :0.0000
## 1st Qu.:4.064 1st Qu.:4.641 1st Qu.:0.7931
## Median :5.321 Median :6.055 Median :0.9564
## Mean :5.505 Mean :5.904 Mean :0.8732
## 3rd Qu.:7.111 3rd Qu.:7.315 3rd Qu.:1.0000
## Max. :9.688 Max. :9.673 Max. :1.0000
## NA's :2071 NA's :2071 NA's :66
## x2_property_rights x3a_money_growth x3b_std_inflation x3c_inflation
## Min. :0.9556 Min. :0.000 Min. :0.000 Min. : 0.000
## 1st Qu.:3.9439 1st Qu.:7.867 1st Qu.:7.555 1st Qu.: 8.192
## Median :5.2306 Median :8.697 Median :8.881 Median : 9.106
## Mean :5.2529 Mean :8.235 Mean :8.008 Mean : 8.464
## 3rd Qu.:6.3925 3rd Qu.:9.256 3rd Qu.:9.404 3rd Qu.: 9.574
## Max. :9.2783 Max. :9.999 Max. :9.952 Max. :10.000
## NA's :755 NA's :644 NA's :607 NA's :607
## x3d_freedom_own_foreign_currency x3_sound_money x4a_tariffs
## Min. : 0.00 Min. :0.000 Min. : 0.000
## 1st Qu.: 0.00 1st Qu.:6.604 1st Qu.: 6.209
## Median : 5.00 Median :7.969 Median : 7.480
## Mean : 5.92 Mean :7.661 Mean : 7.079
## 3rd Qu.:10.00 3rd Qu.:9.257 3rd Qu.: 8.334
## Max. :10.00 Max. :9.922 Max. :10.000
## NA's :621 NA's :611 NA's :681
## x4b_regulatory_trade_barriers x4c_black_market
## Min. :0.000 Min. : 0.000
## 1st Qu.:5.463 1st Qu.:10.000
## Median :6.592 Median :10.000
## Mean :6.333 Mean : 9.115
## 3rd Qu.:7.516 3rd Qu.:10.000
## Max. :9.833 Max. :10.000
## NA's :1348 NA's :617
## x4d_control_movement_capital_ppl x4_trade x5a_credit_market_reg
## Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 2.000 1st Qu.: 5.947 1st Qu.: 6.800
## Median : 4.769 Median : 7.011 Median : 8.306
## Mean : 4.376 Mean : 6.720 Mean : 7.732
## 3rd Qu.: 6.493 3rd Qu.: 7.916 3rd Qu.: 9.333
## Max. :10.000 Max. :10.000 Max. :10.000
## NA's :592 NA's :691 NA's :619
## x5b_labor_market_reg x5c_business_reg x5_regulation
## Min. :1.837 Min. :2.010 Min. :1.002
## 1st Qu.:5.073 1st Qu.:5.387 1st Qu.:5.878
## Median :6.197 Median :6.170 Median :6.759
## Mean :6.168 Mean :6.189 Mean :6.638
## 3rd Qu.:7.344 3rd Qu.:7.007 3rd Qu.:7.486
## Max. :9.725 Max. :9.504 Max. :9.440
## NA's :1158 NA's :1402 NA's :728Variable Description:
Area 1:
- Size of Government—As government spending, taxation, and the size of government-controlled enterprises increase, government decision-making is substituted for individual choice and economic freedom is reduced.
Area 2:
- Legal System and Property Rights—Protection of persons and their rightfully acquired property is a central element of both economic freedom and civil society. Indeed, it is the most important function of government.
Area 3:
- Sound Money—Inflation erodes the value of rightfully earned wages and savings. Sound money is thus essential to protect property rights. When inflation is not only high but also volatile, it becomes difficult for individuals to plan for the future and thus use economic freedom effectively.
Area 4:
- Freedom to Trade Internationally—Freedom to exchange—in its broadest sense, buying, selling, making contracts, and so on—is essential to economic freedom, which is reduced when freedom to exchange does not include businesses and individuals in other nations.
Area 5:
- Regulation—Governments not only use a number of tools to limit the right to exchange internationally, they may also develop onerous regulations that limit the right to exchange, gain credit, hire or work for whom you wish, or freely operate your business.
Creating Data Frame for 2016
Next we will create a data frame for 2016 our most recent year. From there we will do some plotting to get a better view of what has occured over time.
freedom2016 <- filter(freedom, year == "2016") #Filtering to 2016 most recent year in data
freedom2016 <- freedom2016[order(freedom2016$rank),]#Sorting data frame from lowest to highest
head(freedom2016)## # A tibble: 6 x 36
## year iso_code countries economic_freedom rank quartile x1a_government_~
## <dbl> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
## 1 2016 HKG Hong Kong 8.97 1 1 7.92
## 2 2016 SGP Singapore 8.84 2 1 4.82
## 3 2016 NZL New Zeal~ 8.49 3 1 4.62
## 4 2016 CHE Switzerl~ 8.39 4 1 6.4
## 5 2016 IRL Ireland 8.07 5 1 3.74
## 6 2016 USA United S~ 8.03 6 1 6.71
## # ... with 29 more variables: x1b_transfers <dbl>, x1c_gov_enterprises <dbl>,
## # x1d_top_marg_tax_rate <dbl>, x1_size_government <dbl>,
## # x2a_judicial_independence <dbl>, x2b_impartial_courts <dbl>,
## # x2c_protection_property_rights <dbl>, x2d_military_interference <dbl>,
## # x2e_integrity_legal_system <dbl>, x2f_legal_enforcement_contracts <dbl>,
## # x2g_restrictions_sale_real_property <dbl>, x2h_reliability_police <dbl>,
## # x2i_business_costs_crime <dbl>, x2j_gender_adjustment <dbl>,
## # x2_property_rights <dbl>, x3a_money_growth <dbl>, x3b_std_inflation <dbl>,
## # x3c_inflation <dbl>, x3d_freedom_own_foreign_currency <dbl>,
## # x3_sound_money <dbl>, x4a_tariffs <dbl>,
## # x4b_regulatory_trade_barriers <dbl>, x4c_black_market <dbl>,
## # x4d_control_movement_capital_ppl <dbl>, x4_trade <dbl>,
## # x5a_credit_market_reg <dbl>, x5b_labor_market_reg <dbl>,
## # x5c_business_reg <dbl>, x5_regulation <dbl>summary(freedom2016)## year iso_code countries economic_freedom
## Min. :2016 Length:162 Length:162 Min. :2.880
## 1st Qu.:2016 Class :character Class :character 1st Qu.:6.260
## Median :2016 Mode :character Mode :character Median :6.905
## Mean :2016 Mean :6.795
## 3rd Qu.:2016 3rd Qu.:7.468
## Max. :2016 Max. :8.970
##
## rank quartile x1a_government_consumption x1b_transfers
## Min. : 1.00 Min. :1.000 Min. : 0.000 Min. : 2.010
## 1st Qu.: 41.25 1st Qu.:2.000 1st Qu.: 4.122 1st Qu.: 6.295
## Median : 81.50 Median :2.500 Median : 5.665 Median : 8.135
## Mean : 81.27 Mean :2.506 Mean : 5.597 Mean : 7.646
## 3rd Qu.:121.75 3rd Qu.:3.750 3rd Qu.: 7.329 3rd Qu.: 9.461
## Max. :162.00 Max. :4.000 Max. :10.000 Max. :10.000
## NA's :11
## x1c_gov_enterprises x1d_top_marg_tax_rate x1_size_government
## Min. : 0.000 Min. : 1.000 Min. :3.617
## 1st Qu.: 4.000 1st Qu.: 5.000 1st Qu.:5.661
## Median : 7.000 Median : 6.750 Median :6.532
## Mean : 6.287 Mean : 6.519 Mean :6.484
## 3rd Qu.: 8.000 3rd Qu.: 8.375 3rd Qu.:7.410
## Max. :10.000 Max. :10.000 Max. :9.528
## NA's :5
## x2a_judicial_independence x2b_impartial_courts x2c_protection_property_rights
## Min. :0.2168 Min. :0.6413 Min. :1.149
## 1st Qu.:3.4160 1st Qu.:3.0405 1st Qu.:4.529
## Median :4.5898 Median :4.0325 Median :5.445
## Mean :4.9706 Mean :4.2046 Mean :5.635
## 3rd Qu.:6.4326 3rd Qu.:5.2664 3rd Qu.:6.527
## Max. :9.6975 Max. :7.9810 Max. :9.288
## NA's :10 NA's :10
## x2d_military_interference x2e_integrity_legal_system
## Min. : 0.000 Min. : 1.667
## 1st Qu.: 4.167 1st Qu.: 4.167
## Median : 6.667 Median : 5.833
## Mean : 6.345 Mean : 6.058
## 3rd Qu.: 8.333 3rd Qu.: 8.333
## Max. :10.000 Max. :10.000
## NA's :25
## x2f_legal_enforcement_contracts x2g_restrictions_sale_real_property
## Min. :0.000 Min. :2.009
## 1st Qu.:3.376 1st Qu.:6.615
## Median :4.353 Median :7.778
## Mean :4.310 Mean :7.526
## 3rd Qu.:5.339 3rd Qu.:8.695
## Max. :7.661 Max. :9.981
## NA's :2
## x2h_reliability_police x2i_business_costs_crime x2j_gender_adjustment
## Min. :1.396 Min. :0.7782 Min. :0.4146
## 1st Qu.:4.210 1st Qu.:4.6760 1st Qu.:0.7866
## Median :5.572 Median :5.7466 Median :0.9231
## Mean :5.697 Mean :5.7212 Mean :0.8658
## 3rd Qu.:7.432 3rd Qu.:6.9157 3rd Qu.:1.0000
## Max. :9.688 Max. :9.0224 Max. :1.0000
## NA's :10 NA's :10
## x2_property_rights x3a_money_growth x3b_std_inflation x3c_inflation
## Min. :1.856 Min. :2.768 Min. :0.000 Min. : 0.000
## 1st Qu.:4.003 1st Qu.:8.074 1st Qu.:8.408 1st Qu.: 8.813
## Median :5.100 Median :8.783 Median :9.262 Median : 9.623
## Mean :5.214 Mean :8.596 Mean :8.563 Mean : 8.990
## 3rd Qu.:6.069 3rd Qu.:9.360 3rd Qu.:9.584 3rd Qu.: 9.842
## Max. :8.798 Max. :9.985 Max. :9.899 Max. :10.000
##
## x3d_freedom_own_foreign_currency x3_sound_money x4a_tariffs
## Min. : 0.000 Min. :1.942 Min. : 3.253
## 1st Qu.: 5.000 1st Qu.:7.204 1st Qu.: 6.873
## Median :10.000 Median :8.642 Median : 7.748
## Mean : 6.821 Mean :8.242 Mean : 7.489
## 3rd Qu.:10.000 3rd Qu.:9.397 3rd Qu.: 8.266
## Max. :10.000 Max. :9.922 Max. :10.000
## NA's :1
## x4b_regulatory_trade_barriers x4c_black_market
## Min. :0.000 Min. : 0.000
## 1st Qu.:4.330 1st Qu.:10.000
## Median :5.928 Median :10.000
## Mean :5.813 Mean : 9.688
## 3rd Qu.:7.597 3rd Qu.:10.000
## Max. :9.729 Max. :10.000
## NA's :1
## x4d_control_movement_capital_ppl x4_trade x5a_credit_market_reg
## Min. :1.154 Min. :2.877 Min. : 3.333
## 1st Qu.:3.907 1st Qu.:6.357 1st Qu.: 7.410
## Median :5.341 Median :7.169 Median : 8.596
## Mean :5.115 Mean :7.018 Mean : 8.219
## 3rd Qu.:6.619 3rd Qu.:7.952 3rd Qu.: 9.386
## Max. :9.233 Max. :9.324 Max. :10.000
##
## x5b_labor_market_reg x5c_business_reg x5_regulation
## Min. :2.107 Min. :2.010 Min. :2.484
## 1st Qu.:5.328 1st Qu.:5.799 1st Qu.:6.475
## Median :6.470 Median :6.385 Median :7.060
## Mean :6.376 Mean :6.454 Mean :7.016
## 3rd Qu.:7.367 3rd Qu.:7.246 3rd Qu.:7.714
## Max. :9.373 Max. :9.273 Max. :9.440
## #options(repr.plot.width=8, repr.plot.height=10)Visualize our Data
The below chart has each country in our data set and their score over time 1-10. We can see from our plots that some countries were not established in certain periods. This means we will have to deal with NA values in our analysis. Keep this in mind.
#Plot Below Covers All Countries and Year to get a view of changes
freedom %>% filter(!is.na(economic_freedom) | !is.na(year)) %>% group_by(year) %>%
ggplot(aes(year,economic_freedom, fill = economic_freedom, group = 1))+
geom_line(aes(color = economic_freedom))+
scale_color_viridis(option = "plasma",direction = -1, discrete=FALSE) +
facet_wrap(~countries)+theme_bw()+
theme(legend.position = "none", axis.text.x = element_blank(),
strip.text.x = element_text(size = 6))+
xlab(" ") + ylab("")+ ggtitle("ECONOMIC FREEDOM OF THE WORLD 1970-2016")## Warning: Removed 4 rows containing missing values (geom_path).
Scatter Plots
The next three plots show the relation of x (Trade, Sound Money, and Regulations) to economic freedom. The size of the bubble represents the rank. Larger bubbles indicates a higher rank.
Please note a separate file will be send for the video
#Yearly Scatter Plot for US, Potentially other countries
p <- ggplot(freedom, aes(x4_trade, economic_freedom, color = countries)) +
geom_point(aes(size = -rank, frame = year, ids = countries)) +
scale_x_log10()
p <- ggplotly(p)
pp4 <- ggplot(freedom, aes(x3_sound_money, economic_freedom, color = countries)) +
geom_point(aes(size = -rank, frame = year, ids = countries)) +
scale_x_log10()
p4 <- ggplotly(p4)
p4p5 <- ggplot(freedom, aes(x5c_business_reg, economic_freedom, color = countries)) +
geom_point(aes(size = -rank, frame = year, ids = countries)) +
scale_x_log10()
p5 <- ggplotly(p5)
p5Selected Countries Plot
After reviewing our initial line graphs we selected a few countries to show 6 countries trends. Our x-axis is time and y-axis is Economic Freedom
# Keep only 3 names
country <- filter(freedom,countries %in% c("United States", "China", "Venezuela", "United Kingdom", "Ghana","Zimbabwe"))
# Plot
country %>%
ggplot( aes(x=year, y=economic_freedom, group=countries, color=countries)) +
geom_line() +
geom_point() +
scale_color_viridis(discrete = TRUE) +
ggtitle("Countries Performance Over Time") +
theme_ipsum() +
ylab("Economic Freedom") +
transition_reveal(year)
# Save at gif:
anim_save("Economic Freedom by Year.gif")Economic Freedom Bubble Plot Here we can see the distribution of our
##WORK IN PROGRESS NEED TO UPDATE
#static 2016 Scatter Plot
a1 <- ggplotly(ggplot(freedom2016, aes(quartile,economic_freedom , size = -rank)) +
geom_jitter(aes(color=countries, alpha=0.5)) +
theme_bw()+ theme(legend.position= "none")+
xlab("Quartile") +
ggtitle("Economic Freedom Index 2016"), tooltip = c("countries"))
a12016 Maps (Rank and Trade)
From both of these visualizations we can see that trade and economic_freedom are visually similar to rank. The differences do indicate the other variables should be considered when trying to increase the rank profile of a country.
jBrewColors <- brewer.pal(n = 8, name = "BuPu")
p1 <- plot_geo(freedom2016) %>%
add_trace(z = ~-rank, color = ~-rank,colors = jBrewColors,
text = ~freedom2016$countries, locations = ~freedom2016$iso_code) %>%
colorbar(title = 'Countries' , tickprefix = 'Rank') %>%
layout(title = 'Economic Freedom 2016 by Rank')
p1p2 <- plot_geo(freedom2016) %>%
add_trace(z = ~x5c_business_reg, color = ~x5c_business_reg,colors = jBrewColors,
text = ~freedom2016$countries, locations = ~freedom2016$iso_code) %>%
colorbar(title = 'Countries' , tickprefix = 'Trade') %>%
layout(title = 'Economic Freedom 2016 by Trade')
p2p8 <- plot_geo(freedom2016) %>%
add_trace(z = ~economic_freedom, color = ~-rank,colors = jBrewColors,
text = ~freedom2016$countries, locations = ~freedom2016$iso_code) %>%
colorbar(title = 'Countries' , tickprefix = 'Rank') %>%
layout(title = 'Economic Freedom 2016 by Rank')
p8Assigning Clusters For 2016
fviz_nbclust(na.omit(freedom2016[4:36]), kmeans, method = "silhouette")
gap_stat <- clusGap(na.omit(freedom2016[4:36]), FUN = kmeans, nstart = 25,
K.max = 10, B = 50)
fviz_gap_stat(gap_stat)
n_cluster <- 4
results <- kmeans(na.omit(freedom2016[4:36]),n_cluster)
results## K-means clustering with 4 clusters of sizes 26, 34, 32, 29
##
## Cluster means:
## economic_freedom rank quartile x1a_government_consumption x1b_transfers
## 1 6.701923 92.53846 2.807692 5.643794 7.660434
## 2 7.827353 18.85294 1.000000 4.848356 6.391209
## 3 5.793438 135.87500 3.812500 6.300299 8.580960
## 4 7.292759 53.82759 1.931034 5.677600 7.186032
## x1c_gov_enterprises x1d_top_marg_tax_rate x1_size_government
## 1 6.000000 6.923077 6.556826
## 2 8.676471 5.941176 6.464303
## 3 4.468750 5.984375 6.333596
## 4 7.448276 6.137931 6.612460
## x2a_judicial_independence x2b_impartial_courts x2c_protection_property_rights
## 1 4.531053 3.992858 5.283979
## 2 6.897442 5.333483 7.279879
## 3 3.502248 3.442479 4.446322
## 4 5.166858 4.198570 5.889236
## x2d_military_interference x2e_integrity_legal_system
## 1 6.025641 5.544872
## 2 8.774510 7.990196
## 3 4.375000 4.791667
## 4 7.270115 6.063218
## x2f_legal_enforcement_contracts x2g_restrictions_sale_real_property
## 1 4.447582 7.508096
## 2 5.321731 8.311222
## 3 3.265367 6.470558
## 4 4.532511 7.809283
## x2h_reliability_police x2i_business_costs_crime x2j_gender_adjustment
## 1 5.067634 5.386412 0.8680815
## 2 7.567842 6.920993 0.9669095
## 3 4.507362 4.774881 0.7815347
## 4 5.703705 5.593773 0.9143553
## x2_property_rights x3a_money_growth x3b_std_inflation x3c_inflation
## 1 4.922193 8.625213 8.740109 8.919356
## 2 7.048105 8.780676 9.541676 9.776266
## 3 3.906946 8.556711 7.586815 7.543010
## 4 5.535438 8.668712 9.216567 9.465114
## x3d_freedom_own_foreign_currency x3_sound_money x4a_tariffs
## 1 6.346154 8.157708 7.391465
## 2 10.000000 9.524654 8.224081
## 3 3.906250 6.898196 6.813615
## 4 9.655172 9.251391 7.827085
## x4b_regulatory_trade_barriers x4c_black_market
## 1 5.682171 9.982093
## 2 7.880651 10.000000
## 3 4.061851 8.989404
## 4 6.552729 10.000000
## x4d_control_movement_capital_ppl x4_trade x5a_credit_market_reg
## 1 4.955593 7.002831 8.061171
## 2 6.771267 8.219000 9.178555
## 3 3.791417 5.914072 6.914557
## 4 6.230559 7.652593 8.815506
## x5b_labor_market_reg x5c_business_reg x5_regulation
## 1 6.225815 6.316754 6.867913
## 2 6.872708 7.586695 7.879319
## 3 5.572057 5.261378 5.915998
## 4 6.770012 6.650672 7.412063
##
## Clustering vector:
## [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4
## [38] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 1 1 1 1 1 1 1 1 1 1
## [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [112] 3 3 3 3 3 3 3 3 3 3
##
## Within cluster sum of squares by cluster:
## [1] 5140.445 5007.579 9203.978 4697.174
## (between_SS / total_SS = 91.2 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"freedom2016 <- na.omit(freedom2016)
freedom2016$cluster_number <- results$clusterAssigning Clusters for All Years
fviz_nbclust(na.omit(freedom[4:36]), kmeans, method = "silhouette")
gap_stat <- clusGap(na.omit(freedom[4:36]), FUN = kmeans, nstart = 25,
K.max = 10, B = 50)
fviz_gap_stat(gap_stat)
n_cluster <- 4
results2 <- kmeans(na.omit(freedom[4:36]),n_cluster)
results2## K-means clustering with 4 clusters of sizes 385, 259, 314, 358
##
## Cluster means:
## economic_freedom rank quartile x1a_government_consumption x1b_transfers
## 1 7.822883 17.76364 1.002597 4.794888 6.327232
## 2 5.726757 130.15830 3.857143 6.486306 8.503878
## 3 6.625605 90.08280 2.917197 5.914559 7.845109
## 4 7.226285 53.06425 1.930168 5.600535 7.195419
## x1c_gov_enterprises x1d_top_marg_tax_rate x1_size_government
## 1 8.550649 5.902597 6.393842
## 2 4.146718 5.918919 6.263955
## 3 6.305732 6.761146 6.706637
## 4 7.617318 6.449721 6.715748
## x2a_judicial_independence x2b_impartial_courts x2c_protection_property_rights
## 1 7.106385 6.126717 7.596226
## 2 3.177699 3.367870 4.208899
## 3 4.391869 4.158129 5.249542
## 4 4.903138 4.306861 5.795554
## x2d_military_interference x2e_integrity_legal_system
## 1 8.807899 8.218625
## 2 4.299073 4.930022
## 3 6.034143 5.656171
## 4 7.692988 6.162228
## x2f_legal_enforcement_contracts x2g_restrictions_sale_real_property
## 1 5.816585 8.384423
## 2 3.613266 6.326609
## 3 4.392753 7.317927
## 4 4.557858 7.642644
## x2h_reliability_police x2i_business_costs_crime x2j_gender_adjustment
## 1 7.533995 7.269152 0.9652184
## 2 4.123892 4.915084 0.8238479
## 3 4.746553 5.458198 0.9028994
## 4 5.364499 5.732524 0.9220318
## x2_property_rights x3a_money_growth x3b_std_inflation x3c_inflation
## 1 7.308987 8.917465 9.227359 9.486486
## 2 3.943435 7.922469 7.231142 7.818829
## 3 4.997103 8.346155 8.465144 8.748987
## 4 5.555794 8.616402 8.737107 9.047933
## x3d_freedom_own_foreign_currency x3_sound_money x4a_tariffs
## 1 9.974026 9.401334 8.136390
## 2 3.030888 6.500832 6.712690
## 3 5.589172 7.787364 7.155248
## 4 9.511173 8.978154 7.866255
## x4b_regulatory_trade_barriers x4c_black_market
## 1 7.826377 10.000000
## 2 4.766509 8.970826
## 3 6.130137 9.900482
## 4 6.566989 10.000000
## x4d_control_movement_capital_ppl x4_trade x5a_credit_market_reg
## 1 6.610393 8.143290 9.212191
## 2 3.474387 5.981103 7.212481
## 3 4.568715 6.938646 8.118631
## 4 6.010345 7.610897 8.771564
## x5b_labor_market_reg x5c_business_reg x5_regulation
## 1 6.903759 7.485554 7.867168
## 2 5.594121 5.031458 5.946020
## 3 6.022475 5.952039 6.697715
## 4 6.665918 6.375392 7.270958
##
## Clustering vector:
## [1] 1 2 2 2 1 1 1 3 1 2 4 2 4 2 4 2 2 1 1 3 3 2 1 2 3 1 1 1 4 2 2 4 1 2 1 4 2
## [38] 4 1 3 3 1 3 4 1 4 4 3 4 2 1 4 4 4 4 4 4 4 1 3 1 3 3 1 1 2 2 3 2 1 3 3 4 2
## [75] 2 2 1 1 4 2 1 3 2 1 2 3 4 4 4 4 1 3 2 3 2 1 4 4 3 1 3 2 4 1 2 1 3 3 3 2 3
## [112] 4 2 4 1 1 4 2 2 3 2 1 2 2 2 1 1 1 2 4 2 4 2 4 2 4 2 2 1 1 2 3 2 4 2 3 1 4
## [149] 1 4 2 2 4 1 2 1 4 2 4 1 3 2 1 3 4 1 4 4 3 3 1 4 4 4 4 4 4 4 1 3 1 3 1 1 2
## [186] 2 4 2 1 3 3 4 2 2 3 1 1 4 2 1 3 2 1 2 3 4 4 4 1 1 3 2 3 2 1 4 4 3 1 3 3 1
## [223] 1 2 1 3 3 3 2 3 4 2 4 1 1 4 2 2 3 2 4 2 2 2 1 1 1 2 4 2 1 2 4 2 4 2 2 1 1
## [260] 2 3 4 2 3 4 4 1 4 2 2 4 1 2 1 4 2 4 1 2 3 1 3 4 1 4 4 2 3 1 4 4 4 1 1 4 4
## [297] 1 3 1 3 1 1 2 2 3 2 1 3 3 4 2 2 3 1 1 4 2 1 3 2 4 2 3 4 4 4 1 1 3 2 3 2 1
## [334] 4 3 3 4 3 3 1 1 2 1 3 3 3 3 3 4 2 1 1 1 4 2 3 3 2 4 2 2 2 1 1 1 2 4 2 4 3
## [371] 4 2 4 2 2 1 1 2 3 2 1 2 3 4 4 1 4 2 2 4 1 2 1 4 2 4 1 3 3 1 2 4 1 4 3 2 3
## [408] 1 4 4 4 1 1 4 4 4 3 1 3 1 1 3 2 4 2 1 3 3 4 2 2 3 1 1 4 2 1 3 2 4 3 3 1 1
## [445] 4 1 1 3 2 3 2 1 4 3 4 4 3 3 1 1 2 1 3 3 3 2 3 4 2 1 1 1 4 2 2 3 2 4 2 2 2
## [482] 1 1 1 2 4 2 4 3 4 2 4 2 2 1 1 2 3 1 2 3 1 4 1 4 2 2 4 1 2 1 4 2 3 1 3 3 4
## [519] 2 4 1 4 3 3 3 2 1 4 4 4 1 1 4 4 1 3 1 3 1 1 3 2 3 2 1 3 3 4 2 2 3 1 1 4 2
## [556] 1 4 2 4 3 1 4 4 4 1 3 2 3 2 1 4 3 3 4 3 1 1 2 1 3 3 3 3 4 4 2 1 1 1 4 2 2
## [593] 4 2 4 2 2 2 1 1 1 2 1 2 4 2 4 3 4 2 2 1 1 2 3 1 2 3 1 4 1 4 2 2 4 1 2 1 4
## [630] 2 4 1 3 3 4 2 4 1 4 3 3 3 2 1 4 4 4 1 1 3 3 1 3 4 4 1 1 2 3 3 2 1 3 3 4 3
## [667] 2 3 1 1 4 2 1 3 2 4 3 1 4 4 4 4 3 2 3 2 1 1 3 4 1 3 1 1 2 1 3 3 3 3 4 4 2
## [704] 1 1 1 4 2 2 4 2 4 2 2 1 1 1 2 1 3 1 3 4 3 4 2 1 1 2 3 4 2 3 1 4 1 4 2 3 4
## [741] 1 2 1 1 1 3 3 4 2 4 1 4 3 3 3 2 1 4 4 4 1 1 3 3 1 4 4 4 1 1 3 2 3 3 3 4 3
## [778] 2 3 1 1 4 2 1 4 2 4 3 1 4 4 4 4 3 2 3 1 1 3 4 4 3 1 1 2 1 3 3 3 3 3 1 2 1
## [815] 1 1 4 2 4 2 4 2 2 1 1 1 2 4 3 4 3 3 3 4 2 1 1 3 3 1 2 3 1 4 1 4 2 3 1 1 2
## [852] 1 1 1 3 4 4 4 1 4 4 3 3 2 1 4 4 4 1 4 4 4 4 4 4 1 1 3 3 3 3 3 4 3 4 1 1 4
## [889] 2 1 4 3 4 3 1 3 4 4 1 3 2 3 1 1 4 3 4 3 1 1 2 1 3 3 3 3 3 4 2 1 1 1 4 2 4
## [926] 2 4 2 1 1 1 3 1 3 4 3 4 3 4 2 1 1 3 3 4 2 3 1 4 1 3 2 3 1 1 2 1 1 1 3 4 4
## [963] 4 1 4 4 3 3 1 4 4 4 1 4 4 3 1 4 1 1 1 3 3 3 3 3 3 4 1 1 4 2 1 4 2 4 3 1 3
## [1000] 4 4 4 3 2 3 1 1 4 3 4 3 1 1 2 1 3 3 3 4 4 2 1 1 1 4 2 4 2 4 3 4 1 1 2 4 2
## [1037] 4 3 4 3 4 2 1 1 3 3 1 2 3 1 4 1 3 2 3 1 1 2 1 4 1 3 4 4 4 1 4 1 3 3 1 4 4
## [1074] 4 1 4 4 4 1 4 1 1 1 2 3 3 3 4 3 4 1 1 4 3 1 4 2 1 3 4 3 3 4 1 3 2 3 1 1 4
## [1111] 4 1 3 4 1 2 1 3 3 3 3 4 2 1 1 1 4 2 4 2 4 2 4 1 1 3 4 3 4 3 4 3 4 2 1 1 3
## [1148] 3 1 3 4 1 3 2 3 1 1 2 1 4 1 4 4 4 1 4 1 3 3 1 4 4 1 1 4 4 4 1 4 1 1 1 2 3
## [1185] 3 3 4 3 3 1 1 3 1 4 3 3 4 4 4 4 4 2 1 1 4 4 1 3 1 1 1 3 3 3 3 4 2 1 1 1 4
## [1222] 2 4 2 4 3 4 1 1 3 3 1 3 4 3 4 2 1 1 3 3 1 3 4 1 3 2 3 1 1 2 1 4 1 4 4 4 1
## [1259] 4 1 3 3 1 4 4 1 1 4 4 4 1 4 1 4 1 2 3 3 3 3 1 1 4 1 3 1 3 4 4 4 4 4 3 3 1
## [1296] 1 4 4 1 3 1 1 1 3 4 3 3 4 2 4 1 1 4 2 3 2
##
## Within cluster sum of squares by cluster:
## [1] 57728.68 67854.57 62085.51 60041.22
## (between_SS / total_SS = 90.1 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"freedom <- na.omit(freedom)
freedom$cluster_number <- results2$clusterCluster Plots 2016
Note to Megan correct the color to be specific to each cluster not scale
fviz_cluster(results, data = na.omit(freedom2016[4:36]))
jBrewColors2 <- brewer.pal(n = 8, name = "Spectral")
p3 <- plot_geo(freedom2016) %>%
add_trace(z = ~cluster_number, color = ~cluster_number,colors = jBrewColors2,
text = ~freedom2016$countries, locations = ~freedom2016$iso_code) %>%
colorbar(title = 'Countries' , tickprefix = 'Clusters') %>%
layout(title = 'Economic Freedom 2016 by Cluster')
p3Animated Map For Cluster
Chunck Above trying to solve the same problem
Regression
Now we get into the meat of our analysis. We start be prepping our data for regression. Gathering some test and training data
str(freedom)## Classes 'tbl_df', 'tbl' and 'data.frame': 1316 obs. of 37 variables:
## $ year : num 2016 2016 2016 2016 2016 ...
## $ iso_code : chr "ALB" "DZA" "AGO" "ARG" ...
## $ countries : chr "Albania" "Algeria" "Angola" "Argentina" ...
## $ economic_freedom : num 7.54 4.99 5.17 4.84 7.57 7.98 7.58 6.49 7.56 6.3 ...
## $ rank : num 34 159 155 160 29 10 27 106 30 120 ...
## $ quartile : num 1 4 4 4 1 1 1 3 1 3 ...
## $ x1a_government_consumption : num 8.23 2.15 7.6 5.34 7.26 ...
## $ x1b_transfers : num 7.51 7.82 8.89 6.05 7.75 ...
## $ x1c_gov_enterprises : num 8 0 0 6 8 10 10 0 10 7 ...
## $ x1d_top_marg_tax_rate : num 8 4.5 9.5 4 5 5 3.5 6.5 10 8 ...
## $ x1_size_government : num 7.94 3.62 6.5 5.35 7 ...
## $ x2a_judicial_independence : num 2.67 4.19 1.84 3.69 3.87 ...
## $ x2b_impartial_courts : num 3.15 4.33 1.97 2.93 4.2 ...
## $ x2c_protection_property_rights : num 4.51 4.69 2.51 4.26 5.66 ...
## $ x2d_military_interference : num 8.33 4.17 3.33 7.5 5.83 ...
## $ x2e_integrity_legal_system : num 4.17 5 4.17 3.33 5 ...
## $ x2f_legal_enforcement_contracts : num 4.39 4.51 2.3 3.63 5.2 ...
## $ x2g_restrictions_sale_real_property: num 6.49 6.63 5.46 6.86 9.8 ...
## $ x2h_reliability_police : num 6.93 6.14 3.02 3.39 5.71 ...
## $ x2i_business_costs_crime : num 6.22 6.74 4.29 4.13 7.01 ...
## $ x2j_gender_adjustment : num 0.949 0.821 0.846 0.769 1 ...
## $ x2_property_rights : num 5.07 4.69 2.96 3.9 5.81 ...
## $ x3a_money_growth : num 8.99 6.96 9.39 5.23 9.08 ...
## $ x3b_std_inflation : num 9.48 8.34 4.99 5.22 9.26 ...
## $ x3c_inflation : num 9.74 8.72 3.05 2 9.75 ...
## $ x3d_freedom_own_foreign_currency : num 10 5 5 10 10 10 10 5 10 0 ...
## $ x3_sound_money : num 9.55 7.25 5.61 5.61 9.52 ...
## $ x4a_tariffs : num 8.96 6.87 6.99 6.42 8.55 ...
## $ x4b_regulatory_trade_barriers : num 7.49 2.48 2.02 4.81 7.19 ...
## $ x4c_black_market : num 10 5.56 10 0 10 ...
## $ x4d_control_movement_capital_ppl : num 6.41 1.59 2.04 4.7 6.83 ...
## $ x4_trade : num 8.21 4.13 5.26 3.98 8.14 ...
## $ x5a_credit_market_reg : num 7.1 5.1 7.06 5.42 9.1 ...
## $ x5b_labor_market_reg : num 6.92 5.03 4.56 5.15 6.23 ...
## $ x5c_business_reg : num 6.71 5.68 4.93 5.54 6.8 ...
## $ x5_regulation : num 6.91 5.27 5.52 5.37 7.38 ...
## $ cluster_number : int 1 2 2 2 1 1 1 3 1 2 ...
## - attr(*, "na.action")= 'omit' Named int 9 12 13 15 16 17 19 22 25 26 ...
## ..- attr(*, "names")= chr "9" "12" "13" "15" ...freedom$high_ef <- ifelse(freedom$economic_freedom > 6, 1, 0) # Converting streams to binary data
freedom <- na.omit(freedom)
index_training <- sample(dim(freedom)[1], 40, replace = FALSE) # replace = false will prevent code from selecting same observation twice
training_data <- freedom[index_training, ]
test_data <- freedom[-index_training, ]Since we dont want to randomly select variables to use we will use the Lasso Method for variable selection
typeof(training_data[, 7:36])## [1] "list"X_training <- data.matrix(training_data[, 7:36])
X_test <- data.matrix(test_data[, 7:36])
model_linear_lasso <- cv.glmnet(X_training, training_data$economic_freedom, family="gaussian", nfolds = 10, type.measure = "mse", alpha = 1)
summary(model_linear_lasso)## Length Class Mode
## lambda 42 -none- numeric
## cvm 42 -none- numeric
## cvsd 42 -none- numeric
## cvup 42 -none- numeric
## cvlo 42 -none- numeric
## nzero 42 -none- numeric
## call 7 -none- call
## name 1 -none- character
## glmnet.fit 12 elnet list
## lambda.min 1 -none- numeric
## lambda.1se 1 -none- numericmodel_linear_lasso$lambda## [1] 0.65772163 0.59929145 0.54605205 0.49754229 0.45334200 0.41306835
## [7] 0.37637250 0.34293660 0.31247106 0.28471199 0.25941896 0.23637290
## [13] 0.21537418 0.19624093 0.17880743 0.16292267 0.14844907 0.13526126
## [19] 0.12324502 0.11229628 0.10232018 0.09323034 0.08494801 0.07740147
## [25] 0.07052533 0.06426006 0.05855137 0.05334983 0.04861038 0.04429197
## [31] 0.04035719 0.03677197 0.03350525 0.03052873 0.02781665 0.02534549
## [37] 0.02309387 0.02104227 0.01917293 0.01746966 0.01591771 0.01450362coef(model_linear_lasso, s = 0.4)## 31 x 1 sparse Matrix of class "dgCMatrix"
## 1
## (Intercept) 4.56304805
## x1a_government_consumption .
## x1b_transfers .
## x1c_gov_enterprises .
## x1d_top_marg_tax_rate .
## x1_size_government .
## x2a_judicial_independence .
## x2b_impartial_courts .
## x2c_protection_property_rights .
## x2d_military_interference .
## x2e_integrity_legal_system .
## x2f_legal_enforcement_contracts .
## x2g_restrictions_sale_real_property .
## x2h_reliability_police .
## x2i_business_costs_crime .
## x2j_gender_adjustment .
## x2_property_rights 0.06484596
## x3a_money_growth .
## x3b_std_inflation .
## x3c_inflation .
## x3d_freedom_own_foreign_currency .
## x3_sound_money .
## x4a_tariffs .
## x4b_regulatory_trade_barriers .
## x4c_black_market .
## x4d_control_movement_capital_ppl .
## x4_trade 0.18000302
## x5a_credit_market_reg .
## x5b_labor_market_reg .
## x5c_business_reg .
## x5_regulation 0.09948984coef(model_linear_lasso, s = 500)## 31 x 1 sparse Matrix of class "dgCMatrix"
## 1
## (Intercept) 6.9485
## x1a_government_consumption .
## x1b_transfers .
## x1c_gov_enterprises .
## x1d_top_marg_tax_rate .
## x1_size_government .
## x2a_judicial_independence .
## x2b_impartial_courts .
## x2c_protection_property_rights .
## x2d_military_interference .
## x2e_integrity_legal_system .
## x2f_legal_enforcement_contracts .
## x2g_restrictions_sale_real_property .
## x2h_reliability_police .
## x2i_business_costs_crime .
## x2j_gender_adjustment .
## x2_property_rights .
## x3a_money_growth .
## x3b_std_inflation .
## x3c_inflation .
## x3d_freedom_own_foreign_currency .
## x3_sound_money .
## x4a_tariffs .
## x4b_regulatory_trade_barriers .
## x4c_black_market .
## x4d_control_movement_capital_ppl .
## x4_trade .
## x5a_credit_market_reg .
## x5b_labor_market_reg .
## x5c_business_reg .
## x5_regulation .as.double(coef(model_linear_lasso, s = 0.4))## [1] 4.56304805 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
## [7] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
## [13] 0.00000000 0.00000000 0.00000000 0.00000000 0.06484596 0.00000000
## [19] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
## [25] 0.00000000 0.00000000 0.18000302 0.00000000 0.00000000 0.00000000
## [31] 0.09948984as.double(coef(model_linear_lasso, s = 500))## [1] 6.9485 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## [11] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## [21] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## [31] 0.0000#After Lasso Linear Regression
mlr2 <- lm(economic_freedom ~ x3_sound_money + x4_trade + x5c_business_reg, data = training_data)
anova(mlr2)## Analysis of Variance Table
##
## Response: economic_freedom
## Df Sum Sq Mean Sq F value Pr(>F)
## x3_sound_money 1 12.4509 12.4509 139.149 6.309e-14 ***
## x4_trade 1 5.8537 5.8537 65.420 1.298e-09 ***
## x5c_business_reg 1 4.6241 4.6241 51.678 1.859e-08 ***
## Residuals 36 3.2212 0.0895
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Now that we have our predicted values for our model we want to check how our work.
Provide insights by cluster and prediction points
Finally we plot our linear regression with the variables selected from the variable selection
plot_grid(ggplot(freedom, aes(x3_sound_money, economic_freedom)) +
geom_point(color='#50C878', alpha = 0.5)+
xlab("Sound Money") + ylab("Economic Freedom ")+
geom_smooth(method = lm)+theme_bw(),
ggplot(freedom, aes(x4_trade, economic_freedom)) +
geom_point(color='#50C878', alpha = 0.5)+
xlab("Trade") + ylab("")+
geom_smooth(method = lm)+theme_bw(),
ggplot(freedom, aes(x5c_business_reg, economic_freedom)) +
geom_point(color='#50C878', alpha = 0.5)+
xlab("Business_Regulations") + ylab("")+
geom_smooth(method = lm)+theme_bw(),align = 'h')
Conclusion/ Key Takeaways
Note to Group: We can certainly change these as everyone becomes familiar with the data and forms their own takeaways
Dealing with a long time frame created the challenge of dealing with null values.
Cluster 2 had the key attributes of countries that ranked the highests.
Since the aspects of Economic Freedom have been broken down into measurable variables we were able to build sound models
Our models proved to be significant in predicting economic freedom or rank (update this later). If government officials want to improve the lives of their citizens through economic freedom they should focus on: * Having sound money * Free Trade * Business Regulation